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Proof step 4 from proof add-scale-neq (previous step)

⊦ dec_i.scale = dec_j.scale, mkDecimal(dec_i.int * 10 ^ dec_j.scale + dec_j.int * 10 ^ dec_i.scale, dec_i.scale + dec_j.scale).scale = max(dec_i.scale, dec_j.scale)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ ¬ maxScale(i) ≤ abs(j) → mkDecimal(i, j).scale = 0
Proof step 6:
¬ ¬ maxScale(dec_i.int * 10 ^ dec_j.scale + dec_j.int * 10 ^ dec_i.scale) ≤ abs(dec_i.scale + dec_j.scale) ⊦ dec_i.scale = dec_j.scale, mkDecimal(dec_i.int * 10 ^ dec_j.scale + dec_j.int * 10 ^ dec_i.scale, dec_i.scale + dec_j.scale).scale = max(dec_i.scale, dec_j.scale)
Proof step 76:
¬ maxScale(dec_i.int * 10 ^ dec_j.scale + dec_j.int * 10 ^ dec_i.scale) ≤ abs(dec_i.scale + dec_j.scale) ⊦ dec_i.scale = dec_j.scale, 0 = max(dec_i.scale, dec_j.scale)

Rule argument

spec: decimal inst: name: mkDecimal-maxScale-nle-scale seq: ⊦ ¬ maxScale(i) ≤ abs(j) → mkDecimal(i, j).scale = 0 subst: [j, i] → [dec_i.scale + dec_j.scale, dec_i.int * 10 ^ dec_j.scale + dec_j.int * 10 ^ dec_i.scale] flags: rewrite

Additional information

Used terms: dec_i.scale + dec_j.scale, dec_i.int * 10 ^ dec_j.scale + dec_j.int * 10 ^ dec_i.scale